Fiedler, Bernold Global attractors of one-dimensional parabolic equations: Sixteen examples. (English) Zbl 0814.35056 Tatra Mt. Math. Publ. 4, 67-92 (1994). The author considers global attractors of semiflows generated by dissipative one dimensional parabolic equations \[ u_ t = u_{xx} + f(x,u,u_ x), \quad - 1 < x < 1, \tag{1} \] under Neumann boundary conditions. He lists (describes in terms of number of equilibria, their Morse indices and existing heteroclinic connections) sixteen examples of such attractors that arise if the equation has no more than 9 hyperbolic equilibria. A discussion of general properties of the attractor of (1) is also included. Reviewer: P.Polacik (Bratislava) Cited in 14 Documents MSC: 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35B40 Asymptotic behavior of solutions to PDEs 34D45 Attractors of solutions to ordinary differential equations 35K57 Reaction-diffusion equations 35B32 Bifurcations in context of PDEs Keywords:global attractors; dissipative one dimensional parabolic equations; number of equilibria; heteroclinic connections PDFBibTeX XMLCite \textit{B. Fiedler}, Tatra Mt. Math. Publ. 4, 67--92 (1994; Zbl 0814.35056) Full Text: EuDML